Solve for $x$ : $ 2|x + 7| - 8 = 3|x + 7| + 9 $
Solution: Subtract $ {2|x + 7|} $ from both sides: $ \begin{eqnarray} 2|x + 7| - 8 &=& 3|x + 7| + 9 \\ \\ {- 2|x + 7|} && {- 2|x + 7|} \\ \\ -8 &=& 1|x + 7| + 9 \end{eqnarray} $ Subtract $9$ from both sides: $ \begin{eqnarray} -8 &=& 1|x + 7| + 9 \\ \\ {- 9} && {- 9} \\ \\ -17 &=& 1|x + 7| \end{eqnarray} $ Simplify: $ -17 = |x + 7| $ The absolute value cannot be negative. Therefore, there is no solution.